Capacitors in d.c. Circuits

Understanding Capacitors

• A capacitor is an essential component in an electrical circuit that stores electrical charge.
• It consists of two conductive plates separated by a gap, which allows the storage of electric charge.

Charging a Capacitor

• When a capacitor is charged, electrons on one plate are repelled by electrons on the other plate.
• Electrons from the upper plate move towards the positive terminal of the power supply.

Measuring Capacitance

• To determine the capacitance of a capacitor, you can set up a circuit (circuit 1) with a voltage supply cell, a resistor, and the capacitor.
• The voltage applied to charge the capacitor is measured using a voltmeter.
• The charge accumulated by the capacitor is measured by removing it from circuit 1 and connecting it to a coulomb meter (circuit 2).

Graph Analysis

• By varying the charging voltage and measuring the associated charge, you can create a graph of charge (Q) in coulombs against voltage applied (Vc) in volts.
• The gradient of this graph equals the capacitance (C) of the capacitor.

Energy Stored in a Capacitor

• The area under the Q-Vc graph represents the energy stored by the capacitor.
• This energy can be calculated using the formula:
• Energy (U) = ½ * C * Vc²
  • U is the energy stored in joules.
  • C is the capacitance in farads.
  • Vc is the voltage applied in volts.

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Capacitors in d.c. Circuits

Alternative Energy Formulas

• The energy stored can also be calculated using these equations:
  • $U = \frac{1}{2} \times Q \times Vc$
  • $U = \frac{1}{2} \times C \times Q^2$

Calculations

• For example, if a capacitor is charged with a 5-volt cell:
• (a) The charge stored (Q) can be calculated using $Q = C \times Vc$.
• (b) The energy stored (U) can be calculated using $U = \frac{1}{2} \times C \times Vc^2$.

Key Facts

• The SI unit of charge is the Coulomb (C).
• The SI unit of capacitance is the Farad (F).
• A capacitor with a capacitance of 1 Farad can store 1 Coulomb of charge when the potential difference across it is 1 volt.

Summary

• Capacitors are components in electrical circuits that store charge.
• Their capacitance can be determined by plotting the charge against the voltage applied and calculating the gradient of the graph.
• The energy stored in a capacitor can be calculated using various formulas, all based on capacitance and voltage.